Question

The net requirements of an item over 5 consecutive weeks are 50-0-15-20-20. The inventory carrying cost and ordering cost are Re. 1 per item per week and Rs. 100 per order respectively. Starting inventory is zero. Use “Least Unit Cost Technique” for developing the plan. The cost of the plan (in Rs.) is 
1. 200
2. 250
3. 225
4. 260

Answer 1

Correct Answer - Option 2 : 250

C_h = Rs. 1 per item per week

C_o = Rs. 100 per order

Requirements = 50 – 0 – 15 – 20 – 20

Total cost is the cost of carrying inventory and cost of placing order.

Case (I) only one order of 105 units is placed at starting.

Weeks	Quantity			Cost
	Inventory	Used	Carried forward	Order	Carrying	Total
1.	105 (ordered)	50	55	100	55	155
2.	55	0	55	0	55	55
3.	55	15	40	0	40	40
4.	40	20	20	0	20	20
5.	20	20	0	0	0	0

 

Total cost of plan = 155 + 55 + 40 + 20 = 270 Rs.

Case (II) Now order is placed two times, 50 units at starting and 55 units after 2^nd week.

Weeks	Quantity			Cost
	Inventory	Used	Carried forward	Order	Carrying	Total
1.	50 (ordered)	50	0	100	0	100
2.	0	0	0	0	0	0
3.	55 (ordered)	15	40	100	40	140
4.	40	20	20	0	20	20
5.	20	20	0	0	0	0

 

Total cost of plan = 100 + 140 + 20 = 260 Rs.

Case (III) The order is placed two times, 65 units at starting and 40 units after 3^rd week.

Weeks	Quantity			Cost
	Inventory	Used	Carried forward	Order	Carrying	Total
1.	65 (ordered)	50	15	100	15	115
2.	15	0	15	0	15	15
3.	15	15	0	0	0	0
4.	40 (ordered)	20	20	100	20	120
5.	20	20	0	0	0	0

 

Total cost of plan = 115 + 15 + 120 = 250 Rs.

Case (IV) Now again order is placed two times, 85 units at starting and 20 units after 4^th week.

Weeks	Quantity			Cost
	Inventory	Used	Carried forward	Order	Carrying	Total
1.	85 (ordered)	50	35	100	35	135
2.	35	0	35	0	35	35
3.	35	15	20	0	20	20
4.	20	20	0	0	0	0
5.	20 (ordered)	20	0	100	0	100

Total cost of plan = 135 + 35 + 20 + 100 = 290 Rs.

So, The cost of the plan is least in case (III) & it is 250 Rs.